The Carling Cup winners fired Kenny Dalglish as manager on Wednesday and have moved swiftly in an attempt to replace the Kop legend.
Martinez, 38, kept Wigan in the Premier League once again with a game to spare following a 1-0 win at Blackburn which relegated Rovers.
The Latics had looked dead and buried as recently as March, and Liverpool's US-based owners Fenway Sports Group feel the Spaniard is the man to take them forward after a disappointing 8th-placed finish, just nine points above Wigan.
Wigan chairman Dave Whelan was believed to have advised Martinez, an early favourite to succeed Dalglish, to avoid taking the job at Merseyside if it were offered to him.
But Whelan admitted to several news sources on Thursday that his team manager will enter negotiations to leave the DW.
"It is true," Whelan told The Times. "I don't know the exact timescales of when he is due to meet with the Liverpool owners but I will never stand in Roberto's way."
The 75-year-old still hopes Martínez will choose to stay with Wigan, and told Sky Sports: "When Liverpool sacked Kenny I thought that they would be knocking on the door, and sure enough they have.
"Unfortunately in this day and age of clubs looking for new managers, they all have a list of three or four that they would like to sign and Roberto appears to be on every one of them, but I would love to keep him."